Napolitano announced July 12 that she would resign her position to become the next president of the University of California. While several names have been floated for her replacement, on Capitol Hill, Lute and Allen have the most senior level support.

Sen. Tom Carper (D-DE), the chairman of the Senate Committee on Homeland Security and Governmental Affairs, told The Daily Beast Tuesday that he and committee ranking Republican Tom Coburn (R-OK), would like to see Lute get the job.

“I think Jane Holl Lute would be a terrific candidate, and I urge the president to consider her,” Carper said. “She was a terrific deputy secretary, has an excellent military background, knows a lot about cybersecurity, understands the department, and enjoys the confidence of both Senator Coburn and me.”

A former Army officer, Lute is also a lawyer and scholar who served on the National Security Council during the Clinton administration, as executive vice president of the United Nations Foundation, and as assistant secretary general of the U.N. dealing with peacekeeping operations. Her husband is Deputy National Security Adviser retired Gen. Doug Lute, whom President Obama has nominated to be U.S. ambassador to NATO.

Carper said Lute would get through the Senate quickly and easily. “Her confirmation process would be speedy, and around here speedy would be good,” he said.

Sen. Susan Collins (R-ME), who previously served as ranking Republican on the Homeland Security committee, told The Daily Beast she would like to see Allen get the job. Allen left the Coast Guard in 2010 and now works for Booz Allen Hamilton.

“I think Thad Allen would be an excellent choice. I know him well, I’ve worked with him when he was commandant of the Coast Guard. I saw his work with Katrina and the BP disaster, and I think very highly of him.”

Asked if there were any internal candidate she could support, Collins said there were no standouts.

“There are people I like, but there is no one who immediately comes to mind as being ideally suited.”

Carper described Allen as a “very fine person” and said either Lute or Allen would be fine. “You couldn’t go wrong with either one,” he said.

Collins herself has been mentioned as a possible candidate, but she said she was not interested in the job.

“The White House has not contacted me. I do not expect to be contacted by the White House. I’m very happy to be a senator from Maine, and I’m fully committed to seeking reelection,” she said.